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Are the graph # y=x# and #y=3# perpendicular?

Answer 1

No. #y = x# has a gradient of 1.
#y = 3# is a horizontal line, ie the gradient = 0.
These two lines meet at an angle of 45°

Consider # y = x and y = x# in the form # y = mx + c#

#y = 1x + 0# The slope = 1. It is a diagonal line and a line of symmetry of the cartesian plane. It lies at an inclination of 45°.

#y = 0x + 3# has a gradient of 0.

A vertical line would be perpendicular to a horizontal line - a line with an infinite (undefined) gradient and a line with a zero gradient meet at 90°.

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Answer 2

Kennedy Adams

No, the graphs of (y = x) and (y = 3) are not perpendicular. In order for two lines to be perpendicular, their slopes must be negative reciprocals of each other. The slope of (y = x) is 1, and the slope of (y = 3) is 0. Since 1 and 0 are not negative reciprocals, the lines are not perpendicular.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.